Variable optical retarder

ABSTRACT

A sub-wavelength grating is placed inside a liquid crystal variable optical retarder to reduce polarization dependence of the optical retardation generated by the variable optical retarder. A small thickness of the sub-wavelength grating, as compared to a conventional waveplate, reduces the driving voltage penalty due to the in-cell placement of the sub-wavelength grating.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/962,069, filed Aug. 8, 2013 (now U.S. Pat. No. 9,946,134), whichclaims priority from U.S. Provisional Patent Application No. 61/692,896filed Aug. 24, 2012, which are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to optical retarders, and in particular tovariable optical retarders for imparting a variable phase delay to anoptical beam.

BACKGROUND OF THE INVENTION

Liquid crystal variable optical retarders are used to impart a variableoptical phase delay, and/or change the state of polarization of anoptical beam. In a typical liquid crystal variable optical retarder, afew micrometers thick layer of a liquid crystal fluid is sandwichedbetween two transparent electrodes. When a voltage is applied to theelectrodes, an electric field between the electrodes orients liquidcrystal molecules, which are highly anisotropic. Field-inducedorientation of the liquid crystal molecules changes an effective indexof refraction of the liquid crystal layer, which affects an opticalphase of an optical beam propagating through the liquid crystal layer.When the optical beam is linearly polarized at 45 degrees to apredominant direction of orientation of the liquid crystal moleculestermed “director”, the induced optical phase difference can change thepolarization state of the optical beam, for example, it can rotate thelinear optical polarization. When the optical beam is linearly polarizedalong the predominant direction of orientation of the liquid crystalmolecules, a variable optical phase delay is imparted to the opticalbeam by the variable optical retarder.

Arrays of variable optical retarders can be constructed by arranging anarray of individually controllable pixels under a common liquid crystallayer. When a linearly polarized optical beam illuminates such an arraypre-determined optical phase patterns can be imparted to the beam,allowing variable focusing or steering of the optical beam without anymoving parts. Arrays of variable optical retarders have found a varietyof applications in beam scanning/steering, optical aberrationscorrection, and so on.

One disadvantage of liquid crystal variable retarders is that theytypically require a polarized optical beam for proper operation. Thisdisadvantage, however, is not intrinsic and may be overcome by using anappropriate polarization diversity arrangement. By way of example, G. D.Love in an article entitled “Liquid-Crystal Phase modulator forunpolarized light”, Appl. Opt., Vol. 32, No 13, p. 2222-2223, 1 May1993, disclosed a reflective polarization-insensitive variable opticalretarder. Referring to FIG. 1, a variable optical retarder 10 of Lovehas a quarter-wave plate (QWP) 11 disposed between a liquid crystal cell12 and a mirror 13. In operation, an incoming vertically linearlypolarized (V-LP) optical beam 14 propagates through the liquid crystalcell 12, the quarter-wave plate 11, and is reflected by the mirror 13 topropagate back through the quarter-wave plate 11 and the liquid crystalcell 12. The reflected optical beam is shown at 16. The liquid crystalcell 12 has a director 15 oriented vertically; therefore, the variableoptical phase delay will be imparted on the optical beam 14 on the firstpass, without changing its state of polarization. The quarter-wave plate11 is oriented to change the vertical state of polarization to a lefthand-circular polarization (LH-CP), which accordingly changes to a righthand-circular polarization (RH-CP) upon reflection from the mirror 13.On the second pass, the quarter-wave plate 11 changes the righthand—circular polarization to horizontal linear polarization (H-LP),which will not be changed by the liquid crystal cell 12, since itsdirector 15 is oriented perpendicular to it, that is, is orientedvertically. One can see that, if the incoming optical beam 14 werehorizontally polarized (not shown for simplicity), it would be reflectedvertically polarized and phase-delayed by the same amount, only not onthe first but the second pass through the liquid crystal cell 12.Therefore, if the optical beam 14 were unpolarized or randomlypolarized, it would be phase-delayed by a same amount regardless of itsstate of polarization. Thus, the variable optical retarder 10 ispolarization-insensitive.

One drawback of the variable optical retarder 10 of FIG. 1 is thatplacing the quarter-wave plate 11 between the liquid crystal cell 12 andthe mirror 13 increases a distance D between the mirror 13 and theliquid crystal cell 12. This is detrimental, because the incomingoptical beam 14 diverges while propagating through the distance D. Thebeam divergence increases the beam spot size on the liquid crystal cell12. The increased beam spot size is detrimental in a variable retarderarray configuration, in which the liquid crystal cell 12 is pixilated,because it reduces the spatial resolution.

Another disadvantage of the variable optical retarder 10 is that theliquid crystal cell 12 has to be transmissive to accommodate theexternal quarter-wave plate 11. Transmissive liquid crystal cellsusually have a higher optical loss in a double-pass configuration thanreflective liquid crystal cells in a single-pass configuration, becausein a transmissive cell, the incoming light has to pass twice through twotransparent electrodes. The transparent electrodes have to both conductelectricity and transmit light. These requirements are somewhatcontradictory, and as a result, the transparent electrodes usuallyintroduce some extra optical loss into the system.

James et. al. in an article entitled “Modeling of the diffractionefficiency and polarization sensitivity for a liquid crystal 2D spatiallight modulator for reconfigurable beam steering”, J. Opt. Soc. Am. A.Vol 24, No. 8, p. 2464-2473, discloses a reflectivepolarization-insensitive liquid crystal retarder array, in which one ofthe electrodes is made highly reflective, and the quarter-wave plate isplaced inside the liquid crystal cell. The resulting optical loss islower in this case, because in the James device, the incoming opticalbeam passes twice through a single transparent electrode, not throughtwo electrodes. However, inside placement of the quarter-wave platereduces electrical field across the liquid crystal layer, thus requiringa higher driving voltage to compensate for the electric field decrease.

SUMMARY OF THE INVENTION

It is an objective of the invention to provide a variable opticalretarder, in which the polarization sensitivity would be reduced withoutexcessive optical loss or driving voltage penalties.

In accordance with the invention, a dielectric or semiconductorsub-wavelength grating is placed inside a liquid crystal variableoptical retarder between an electrode and a liquid crystal layer. Thesub-wavelength grating acts as a quarter-wave plate, while having a verysmall thickness, so that the driving voltage penalty due to the in-cellplacement of the sub-wavelength grating is lessened. The sub-wavelengthgrating can also be made highly reflective, for example, it can includea multilayer dielectric high reflector, which further reduces opticalloss in comparison with a metal reflector.

In accordance with one aspect of the invention, there is provided aliquid crystal variable optical retarder comprising:

a first continuous flat electrode;

a second substantially transparent continuous flat electrode opposed tothe first electrode;

a liquid crystal layer having a director and disposed between the firstand second electrodes, for imparting a variable optical phase shift tolight impinging on the second electrode when a voltage is appliedbetween the first and second electrodes; and

a sub-wavelength grating disposed between the liquid crystal layer andthe first electrode and having grating lines at an acute angle,preferably 45 degrees, to the director.

In accordance with the invention, there is further provided a variableoptical retarder for imparting a variable phase delay to an optical beamimpinging thereon, the variable optical retarder comprising:

a substrate having a pixel electrode;

a sub-wavelength grating disposed on and separate from the pixelelectrode, for imparting a first optical retardation to the optical beamimpinging thereon, the sub-wavelength grating having a plurality ofgrating lines running parallel to each other;

a liquid crystal layer on the sub-wavelength grating, for imparting asecond optical retardation to the optical beam propagating therethrough;and

a substantially transparent backplane electrode on the liquid crystallayer;

wherein the second optical retardation is varied when a voltage isapplied between the pixel and backplane electrodes, thereby impartingthe variable phase delay to the optical beam propagating through theliquid crystal layer;

wherein a director of the liquid crystal layer forms an acute angle withthe grating lines, whereby sensitivity of the variable optical retarderto a state of polarization of the optical beam is lessened.

In accordance with another aspect of the invention, there is provided aliquid-crystal-on-silicon spatial light modulator comprising a trimretarder, wherein the trim retarder includes a sub-wavelength grating.

In accordance with yet another aspect of the invention, there is furtherprovided a method for imparting a variable phase delay to a beam oflight, the method comprising:

(a) propagating the beam through a liquid crystal layer and then througha sub-wavelength grating having grating lines oriented at an angle to adirector of the liquid crystal layer;

(b) reflecting the beam propagated in step (a) to propagate the beamback through the liquid crystal layer; and

(c) while performing steps (a) and (b), applying an electric field tothe liquid crystal layer via a pair of flat electrodes external to, andparallel to the liquid crystal layer and the sub-wavelength grating, tovary an optical retardation of the liquid crystal layer, thereby varyingthe phase delay of the beam of light; wherein the flatness of theelectrodes facilitates spatial uniformity of the applied electric field,thereby facilitating spatial uniformity of the varied opticalretardation of the liquid crystal layer.

In a preferred embodiment the sub-wavelength grating does not containany metal, which reduces optical loss and electric field fringing orshielding effects.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments will now be described in conjunction with thedrawings, in which:

FIG. 1 is a schematic view of a prior-art polarization-insensitiveliquid crystal variable optical retarder;

FIGS. 2A and 2B are side and plan cross-sectional views, respectively,of a variable optical retarder of the invention;

FIG. 3A is a side cross-sectional view of an embodiment of the variableoptical retarder of FIGS. 2A and 2B;

FIGS. 3B and 3C are magnified side cross-sectional views of a pixel areaof two embodiments of the variable optical retarder of FIG. 3A;

FIG. 4 is a side cross-sectional view of a liquid-crystal-on-silicon(LCoS) implementation of the variable optical retarder of FIG. 3A;

FIG. 5 is a spatial light modulator having therein a trim retarder inform of a sub-wavelength grating;

FIG. 6 is a flow chart of a method for imparting a variable phase delayto a beam of light according to the invention;

FIG. 7 is a theoretical plot of effective refractive indices,birefringence, and a height of a sub-wavelength grating used in thevariable optical retarders of FIGS. 2A, 2B, and FIGS. 3A to 3C, as afunction of a fill factor of the sub-wavelength features, computed in anapproximation of a grating pitch being much smaller wavelength;

FIG. 8 is the fill factor dependence of an optical retardance,polarization-dependent loss, and insertion loss of an example tantala(Ta₂O₅)—air lamellar grating on aluminum substrate, computed using anelectromagnetic theory at a finite grating pitch of 0.8 micrometers; and

FIG. 9 is a plot of voltage drop across the liquid crystal layer vs.voltage applied to a variable optical retarder having an in-cellsub-wavelength grating, in comparison with a corresponding voltage dropin a variable optical retarder having an in-cell conventionalquarter-wave waveplate in place of the in-cell sub-wavelength grating.

DETAILED DESCRIPTION OF THE INVENTION

While the present teachings are described in conjunction with variousembodiments and examples, it is not intended that the present teachingsbe limited to such embodiments. On the contrary, the present teachingsencompass various alternatives, modifications and equivalents, as willbe appreciated by those of skill in the art. In FIGS. 2A, 2B and 3A, 3B,and 3C, similar numerals refer to similar elements.

Referring to FIGS. 2A and 2B, a variable optical retarder 20 of theinvention includes a first continuous flat electrode 21 and a secondsubstantially transparent continuous flat electrode 22 opposed to thefirst electrode 21, a liquid crystal layer 26, and a sub-wavelengthgrating 24 disposed between the liquid crystal layer 26 and the firstelectrode 21. As seen in FIG. 2B, the sub-wavelength grating 24 has aplurality of grating lines 25 running parallel to each other. A director27 of the liquid crystal layer 26 is at an angle α of 45 degrees withrespect to the grating lines 25. The sub-wavelength grating 24 has aquarter-wavelength retardation in a single pass, amounting to half-waveretardation in a double pass.

In operation, an optical beam 28 impinges onto the liquid crystal layer26 through the second electrode 22. A voltage V is applied between thefirst 21 and second 22 electrodes, thereby varying an opticalretardation of the liquid crystal layer 26. As a result, a variablephase delay is imparted to the optical beam 28. The sub-wavelengthgrating 24 acts as a quarter-wave plate oriented at α=45 degrees to thedirector 27, switching horizontal and vertical polarizations, asexplained above with respect to FIG. 1, which results in lessening asensitivity of the variable optical retarder 20 to a state ofpolarization of the optical beam 28. In some embodiments, the angle α isnot equal to 45 degrees, but remains an acute angle. The retardationvalue of the sub-wavelength grating 24 can deviate from a quarter-wavein a single pass, if some polarization dependence is required.

The flatness and evenness of a top surface 23 of the first electrode 21is beneficial in that the flat and even surface 23 of the firstelectrode 21, for example flat to within 0.2 micron, or preferablywithin 0.1 micron, generates a more even electric field than, forexample, a corrugated surface would, which the first electrode 21 wouldif the sub-wavelength grating 24 were micromachined directly in thefirst electrode 21. A more even electric field is applied to the liquidcrystal layer 26, generating a more uniform optical retardation profileof the liquid crystal layer 26, and thus lessening unwanted anduncontrollable diffraction effects in the liquid crystal layer 26perturbed by fringing electric fields.

The top surface 23 of the first electrode 21 can be made highlyreflective, in which case the sub-wavelength grating 24 is madetransmissive. However, the sub-wavelength grating 24 itself can be madehighly reflective, for example it can include a multilayer dielectrichigh reflector, not shown, so that a high reflectivity of the surface 23of the first electrode 21 is not required. Since metal reflectorsnecessarily incur some optical loss, a high dielectric reflector of thesub-wavelength grating 24 can have a higher reflectivity then thesurface 23 of the first electrode 21, resulting in a lower overalloptical loss of the variable optical retarder 20. To further lower theoptical loss and prevent electrical field shielding, the sub-wavelengthgrating 24 is preferably made of a dielectric or a semiconductor, absentany metal therein; for instance, the sub-wavelength grating 24 caninclude periodic structure of tantala (Ta₂O₅) or silicon (Si) in asilicon dioxide (SiO₂) host.

Referring now to FIGS. 3A and 3B, a variable optical retarder 30 of theinvention includes a substrate 34C having a plurality of pixelelectrodes 31 formed therein, a sub-wavelength grating 34 disposed onand separate from the pixel electrode 31, a liquid crystal layer 36 onthe sub-wavelength grating 34, and a substantially transparent backplaneelectrode 32 on the liquid crystal layer 36. A glass cover plate 39supports the backplane electrode 32, made of indium tin oxide (ITO) orother suitable material. The cover plate 39 has an anti-reflection (AR)coating 39A. Alignment layers 37 adhered to the sub-wavelength grating34 and the backplane electrode 32 are used to align liquid crystalmolecules in the liquid crystal layer 36. The sub-wavelength grating 34has a plurality of grating lines in form of ridges 34A. The liquidcrystal layer 36 extends into gaps 34B between the ridges 34A. In theembodiment shown, the substrate 34C is a silicon dioxide substrate.

In operation, an optical beam 38 propagates in succession through the ARcoating 39A, the cover plate 39, the transparent backplane electrode 32,the liquid crystal layer 36, impinges onto the sub-wavelength grating34, and is reflected by top surfaces 33 of the pixel electrodes 31 topropagate back through the stack in reverse order. The liquid crystallayer 36 and the sub-wavelength grating 34 impart first and secondoptical retardations, respectively, to the optical beam 38. The secondoptical retardation is varied when a voltage is applied between thepixel 31 and backplane 32 electrodes, thereby imparting a variable phasedelay to the optical beam 38 propagating through the liquid crystallayer 36. A director, not shown, of the liquid crystal layer 36 forms a45 degrees angle with the grating lines 34A, whereby sensitivity of thevariable optical retarder 30 to a state of polarization of the opticalbeam 38 is lessened.

Preferably, the top surfaces 33 of the pixel electrodes 31 are flat toavoid fringing electrical fields and associated liquid crystalrefractive index spatial modulation as explained above. To increasereflectivity, the sub-wavelength grating 34 can be made reflective. Alsoin one embodiment, the liquid crystal layer 36 director forms an acuteangle with the grating lines (ridges 34A) not necessarily equal to 45degrees. Shapes of the grating lines other than rectangular ridges 34Acan be used, including triangular, trapezoidal, and the like. Thesub-wavelength grating 34 preferably has an optical retardation of aquarter-wavelength in a single pass, that is, a quarter-wavelengthretardation when the optical beam 38 propagates down in FIG. 3A, plus aquarter-wavelength retardation when the optical beam 38 is reflected topropagate up in FIG. 3A. As explained above w.r.t. the variable opticalretarder 20 of FIG. 2, the sub-wavelength grating 34 of the variableoptical retarder 30 of FIG. 3A preferably includes a dielectric or asemiconductor, and most preferably is a pure dielectric absent any metaltherein for low optical loss and low disturbance to the electric fieldgenerated by the pixel 31 and backplane 32 electrodes. By way of anon-limiting example, the grating lines or ridges 34A of thesub-wavelength grating 34 can be made of tantala (Ta₂O₅).

In an embodiment of the variable optical retarder 30 shown in FIG. 3C,the tantala ridges 34A are formed in the silicon dioxide substrate 34C,which planarizes the sub-wavelength grating 34, so that the loweralignment layer 37 is flat, and, accordingly, the liquid crystal layer36 is flat on both sides. This provides a more stable sub-wavelengthgrating 34, because it does not include a sub-wavelength gratingstructure partially formed by liquid crystal material, as is seen inFIG. 3B.

It is to be understood that, although FIGS. 3A to 3C show a plurality ofpixel electrodes 31 under the common liquid crystal layer 36, thesub-wavelength grating 34, backplane electrode 31, the variable opticalretarder 30 can include only one pixel electrode 31, effectively makingthe variable optical retarder 30 a non-pixilated optical retarder, whichcan be used in applications where the entire optical beam 38 needs to begiven a same variable optical phase shift.

The pixilated variable optical retarders 30 of FIGS. 3A to 3C can beadvantageously implemented in liquid-crystal-on-silicon (LCoS)technology. Referring now to FIG. 4, a LCoS variable optical retarder 40is shown. In the LCoS variable optical retarder 40, the silicon dioxidesubstrate 34C is an overlayer on a silicon substrate 42 having thereon adriver circuitry 41 under the plurality of pixel electrodes 31, forindependently applying a voltage to each of the pixel electrodes 31. Thesilicon driver electronics 41 can be compact, fast, and can accommodatea very large number of the pixel electrodes 31.

Speed and compactness of LCoS technology has resulted in its successfuluse in spatial light modulators for high-definition optical projectorequipment. According to one aspect of the present invention,sub-wavelength gratings can be used in a LCoS-based spatial lightmodulator as a trim retarder. Trim retarders provide a relatively smallbirefringence which, in combination with the voltage-controlledbirefringence of the liquid crystal layer of a LCoS spatial lightmodulator, provides a wider viewing angle and improves image contrast.Turning to FIG. 5, a spatial light modulator 50 includes a siliconsubstrate 52, driver electronics 51, a pixilated variable opticalretarder 55, a sub-wavelength grating trim retarder 54, and an ARcoating 53.

Turning to FIG. 6 with further reference to FIGS. 2A and 2B, a method 60for imparting a variable phase delay to a beam of light includes a step61 of providing the sub-wavelength grating 24; a step 62 of propagatingan optical beam 28 through the liquid crystal layer 26, and then throughthe sub-wavelength grating 24; a step 63 of reflecting the optical beam28 to propagate back through the liquid crystal layer 26; and a step 64of applying an electric field to the liquid crystal layer via the pairsof electrodes 21, 22, to vary an optical retardation of the liquidcrystal layer 26, thereby varying the phase delay of the beam of light28. The flatness of the electrodes 21, 22 facilitates spatial uniformityof the applied electric field, thereby facilitating spatial uniformityof the varied optical retardation of the liquid crystal layer 26.Preferably, the sub-wavelength grating 24 has a quarter-wavelengthoptical retardation in a single pass, and the sub-wavelength gratinglines are disposed at the angle of 45+−5 degrees to the director 27 ofthe liquid crystal layer 26. The method 60 is equally applicable to thevariable optical retarders 30 of FIGS. 3A to 3C.

The optical retardation of the sub-wavelength gratings 24 and 34, and/orthe sub-wavelength grating trim retarder 54 can be calculatedanalytically in an approximation of the grating pitch being much smallerthan the wavelength. Referring to FIG. 7, analytically computedeffective refractive indices for T_(E) and T_(M) polarizations n_(TE) 71and n_(TM) 72, respectively, birefringence Δn 73, and a height 74 of asub-wavelength grating including rectangular ridges having a refractiveindex of 2.2; gaps between the ridges having a refractive index of 1.0,are plotted as a function of a fill factor defined as ridge widthdivided by the grating pitch. The calculation was performed at atelecommunications C-band wavelength of 1.55 micrometers. The maximumvalue for Δn=0.4 is observed at the fill factor of 0.6 at the depth of0.97 micrometers, which corresponds to the optical retardation of0.4*0.97=0.39 micrometers, or approximately one quarter of the C-band1.55 micrometers wavelength. this calculation proves that one quarter ofwavelength retardation is readily achievable at reasonable height 74 ofa sub-wavelength grating.

Turning to FIG. 8, a retardance 83, a polarization-dependent loss (PDL)84, and an insertion loss (IL) 85 are plotted as a function of the abovedefined fill factor for a sub-wavelength grating having 0.97 micrometershigh Ta₂O₅ ridges at the pitch of 0.8 micrometers, disposed on aluminumsubstrate, with air having a refractive index of 1.0 extending into thegrooves between the ridges. The retardance 83 is a difference betweenT_(M)-polarized and T_(E)-polarized zero-order diffracted light phases.One can see that the half-wave retardance occurs at the fill factor ofapproximately 0.46. The PDL is approximately 0.08 dB, and the average ILis approximately 0.2 dB.

The grating structure of FIG. 3B can be modified to accommodate theair-filled grooves. A thin flat membrane, not shown, can be disposed ontop of the grating structure 34, to create and seal the air channels 34Cbetween the grating ridges 34A, thereby preventing the liquid crystalfluid of the layer 36 from filling the air channels 34C, and providing aplanarizing surface for the subsequently disposed alignment layer 37.For example, a SiO₂ membrane can be used for this purpose.

Referring now to FIG. 9 with further reference to FIG. 3B, a voltagedrop across the liquid crystal layer 36 is plotted as a function of thepixel voltage applied between the pixel electrodes 31 and thetransparent backplane electrode 32. A straight line 91 (diamonds)corresponds to a case when a conventional quarter-wave waveplate, notshown, is inserted in place of the sub-wavelength grating 34. A straightline 92 (rectangles) corresponds to the case shown in FIG. 3B, that is,when the sub-wavelength grating 34 is used. One can see that using thesub-wavelength grating 34 approximately doubles the voltage drop acrossthe liquid crystal layer 36 at a same pixel voltage, allowing one toachieve considerably higher levels of variable optical retardation.

The foregoing description of one or more embodiments of the inventionhas been presented for the purposes of illustration and description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed. Many modifications and variations are possiblein light of the above teaching. It is intended that the scope of theinvention be limited not by this detailed description, but rather by theclaims appended hereto.

What is claimed is:
 1. A variable optical retarder comprising: asubstrate; a plurality of electrically separated reflective pixelelectrodes formed in the substrate; a dielectric sub-wavelength opticaldiffractor, having ridges and gaps, that is disposed on and between theplurality of electrically separated reflective pixel electrodes, forimparting a first optical retardation to an optical beam impingingthereon, the ridges and the gaps being separated in a first directionand the dielectric sub-wavelength optical diffractor directly contactingthe substrate between adjacent electrically separated reflective pixelelectrodes in the first direction, the ridges being non-metallic and thegaps being filled with a non-metallic material; a liquid crystal layer,disposed on the dielectric sub-wavelength optical diffractor, forimparting a second optical retardation to the optical beam propagatingthere through; and a substantially transparent backplane electrodedisposed on the liquid crystal layer, wherein the second opticalretardation is varied when a voltage is applied between the plurality ofelectrically separated reflective pixel electrodes and the substantiallytransparent backplane electrode.
 2. The variable optical retarder ofclaim 1, wherein the dielectric sub-wavelength optical diffractor has aplurality of grating lines running parallel to each other.
 3. Thevariable optical retarder of claim 2, wherein a director of the liquidcrystal layer forms an acute angle with the grating lines, wherebysensitivity of the variable optical retarder to a state of polarizationof the optical beam is lessened.
 4. The variable optical retarder ofclaim 1, wherein neither the plurality of electrically separatedreflective pixel electrodes nor the substantially transparent backplaneelectrode includes a portion that extends into the dielectricsub-wavelength optical diffractor.
 5. The variable optical retarder ofclaim 1, wherein the substrate, the ridges, and the plurality ofelectrically separated reflective pixel electrodes are each locatedbelow a flat alignment layer that separates the liquid crystal layerfrom the ridges.
 6. The variable optical retarder of claim 1, whereindriver circuitry is located under the plurality of electricallyseparated reflective pixel electrodes.
 7. The variable optical retarderof claim 6, wherein the driver circuitry applies a voltage to each ofthe plurality of electrically separated reflective pixel electrodes. 8.The variable optical retarder of claim 7, wherein the voltage isindependently applied to each of the plurality of electrically separatedreflective pixel electrodes.
 9. The variable optical retarder of claim7, wherein a first voltage is applied to a first reflective pixelelectrode of the plurality of electrically separated reflective pixelelectrodes, and a second, different voltage is applied to a second,different reflective pixel electrode of the plurality of electricallyseparated reflective pixel electrodes.
 10. The variable optical retarderof claim 9, wherein the application of the first voltage and the second,different voltage creates different phase delays in the second opticalretardation.
 11. The variable optical retarder of claim 1, wherein theplurality of electrically separated reflective pixel electrodes includeflat top surfaces, and wherein the ridges and the gaps are disposed onthe flat top surfaces of the plurality of electrically separatedreflective pixel electrodes.
 12. A variable optical retarder comprising:a substrate; a plurality of electrically separated reflective pixelelectrodes formed in the substrate; a dielectric sub-wavelength opticaldiffractor, having ridges and gaps, that is disposed on and between theplurality of electrically separated reflective pixel electrodes, forimparting a first optical retardation to an optical beam impingingthereon, the ridges and gaps being separated in a first direction andthe dielectric sub-wavelength optical diffractor directly contacting thesubstrate between adjacent electrically separated reflective pixelelectrodes in the first direction, and the ridges being non-metallic andthe gaps being filled with a non-metallic material; wherein theplurality of electrically separated reflective pixel electrodes extenddownward in a direction opposite to the dielectric sub-wavelengthoptical diffractor; a liquid crystal layer, disposed on the dielectricsub-wavelength optical diffractor, for imparting a second opticalretardation to the optical beam propagating there through; and asubstantially transparent backplane electrode disposed on the liquidcrystal layer, wherein the second optical retardation is varied when avoltage is applied between the plurality of electrically separatedreflective pixel electrodes and the substantially transparent backplaneelectrode.
 13. The variable optical retarder of claim 12, wherein thedielectric sub-wavelength optical diffractor has a plurality of gratinglines running parallel to each other.
 14. The variable optical retarderof claim 13, wherein a director of the liquid crystal layer forms anacute angle with the grating lines, whereby sensitivity of the variableoptical retarder to a state of polarization of the optical beam islessened.
 15. The variable optical retarder of claim 12, wherein neitherthe plurality of electrically separated reflective pixel electrodes northe substantially transparent backplane electrode includes a portionthat extends into the dielectric sub-wavelength optical diffractor. 16.The variable optical retarder of claim 12, wherein the substrate and theplurality of electrically separated reflective pixel electrodes are eachlocated below a flat alignment layer that separates the liquid crystallayer from ridges of the dielectric sub-wavelength optical diffractor.17. The variable optical retarder of claim 12, wherein driver circuitryis located under the plurality of electrically separated reflectivepixel electrodes.
 18. The variable optical retarder of claim 17, whereinthe driver circuitry applies a voltage to each of the plurality ofelectrically separated reflective pixel electrodes.
 19. The variableoptical retarder of claim 18, wherein the voltage is independentlyapplied to each of the plurality of electrically separated reflectivepixel electrodes.
 20. The variable optical retarder of claim 18, whereina first voltage is applied to a first reflective pixel electrode of theplurality of electrically separated reflective pixel electrodes, and asecond, different voltage is applied to a second, different reflectivepixel electrode of the plurality of electrically separated reflectivepixel electrodes.
 21. The variable optical retarder of claim 20, whereinthe application of the first voltage and the second, different voltagecreates different phase delays in the second optical retardation. 22.The variable optical retarder of claim 12 wherein the plurality ofelectrically separated reflective pixel electrodes include flat topsurfaces, and wherein the ridges and the gaps are disposed on the flattop surfaces of the plurality of electrically separated reflective pixelelectrodes.